Results 1  10
of
13
THE NONLINEAR SCHRÖDINGER EQUATION WITH A STRONGLY ANISOTROPIC HARMONIC POTENTIAL ∗
"... Abstract. The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The li ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
(Show Context)
Abstract. The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground state of the dominating harmonic oscillator is shown to be propagated, and the lowerdimensional modulation wave function again satisfies a nonlinear Schrödinger equation. The main tools of the analysis are energy and Strichartz estimates, as well as two anisotropic Sobolev inequalities. As an application, the dimension reduction of the threedimensional Gross–Pitaevskii equation is discussed, which models the dynamics of Bose–Einstein condensates.
Diffusive transport of partially quantized particles: existence, uniqueness and long time behaviour
, 2006
"... ..."
Analysis of a quantum subband model for the transport of partially confined charged particles
"... ..."
Analysis of a diffusive effective mass model for nanowires
 Kin. Rel. Models
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Analysis of a diffusive effective mass model for nanowires C. Jourdana∗ † and N. Vauchelet‡ This work is dedicated to Naoufel Ben Abdallah, who was a talented researcher, an enthusiastic supervisor and a generous person. We propose in this paper to derive and analyze a selfconsistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultrascaled confined structure, taking in account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a driftdiffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire DriftDiffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain.
SUB BAND DIFFUSION MODELS FOR QUANTUM TRANSPORT IN A STRONG FORCE REGIME ∗
"... Abstract. We derive semi classical approximations to quantum transport models in thin slabs with applications to SOI (Silicon Oxide on Insulator) type semiconductor devices via a sub band approach. In the regime considered the forces acting on the particles across the slab are much larger than th ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We derive semi classical approximations to quantum transport models in thin slabs with applications to SOI (Silicon Oxide on Insulator) type semiconductor devices via a sub band approach. In the regime considered the forces acting on the particles across the slab are much larger than the forces in the lateral direction of the slab. In a semi classical limit the transport picture can be described on large time scales by a system of sub band convection diffusion equations with an inter band collision operator, modeling the transfer of mass (charge) between the different eigenspaces and driving the system towards a local Maxwellian equilibrium.